The usual models of the chemostat assume that the competition is purely exploitative, the competition is only through the consumption of the nutrient. However, it is known that microorganisms can produce toxins against its competitors. In this work, we consider a model of competition in the chemostat between plasmid-bearing, plasmid-free organisms for a single nutrient where plasmid-bearing org...

A food web in a chemostat is considered in which an arbitrary number of competitor populations compete for a single, essential, nonreproducing, growth-limiting substrate, and an arbitrary number of predator populations prey on some or all of the competitor populations. Although any number of predator populations may prey on the same competitor population, each predator population preys on only ...

This paper deals with a model of a biochemical reactor system with distributed parameters and with a time delay in the growth response. Time delay has been introduced in microbial growth systems to explain the time lapse between the consumption of (liquid) substrate and its conversion to (solid) biomass. We study here the properties of the resulting system of partial functional differential equ...

We establish a general result for estimating the upper average of a continuous and bounded function over an infinite interval. As an application, we show that a previously studied model of microbial growth in a chemostat with time–varying nutrient input admits solutions (populations) that exhibit weak persistence but not weak average persistence.

We study a general single-species chemostat model with non-autonomous input and washout, discrete-time delay between consumption of the nutrient growth. The goal this article is to provide sufficient necessary conditions for persistence. persistence criteria obtained here extend previous works done autonomous without delay. Furthermore, in particular case periodic same washout delayed response ...

In this paper is considered a microalgae growth model under the influence of sunlight. The two-dimensional system first order Ordinary Differential Equations (ODE) with ten-dimensional parameter space. For model, we study existence equilibrium points and their stability, determine bifurcation when value some parameters varied. Lambert w function used to calculate apply linearization technique p...

We revisit the well-known chemostat model, considering that bacteria can be attached together in aggregates or flocs. We distinguish explicitly free and attached compartments in the model and give sufficient conditions for coexistence of these two forms. We then study the case of fast attachment and detachment and shows how it is related to densitydependent growth functions. Finally, we give so...

Microbial populations compete for nutrient resources, and the simplest mathematical models of competition neglect differences in the nutrient content of individuals. The simplest models also assume a spatially uniform habitat. Here both of these assumptions are relaxed. Nutrient content of individuals is assumed proportional to cell size, which varies for populations that reproduce by division,...

Traditional assumptions in the simple chemostat model include fixed availability of the nutrient and its supply rate, and fast flow rate to avoid wall growth. However, these assumptions become unrealistic when the availability of a nutrient depends on the nutrient consumption rate and input nutrient concentration and when the flow rate is not fast enough. In this paper, we relax these assumptio...

We study the global dynamics of n-species competition in a chemo-stat with distributed delay describing the time-lag involved in the conversion of nutrient to viable biomass. The delay phenomenon is modelled by the gamma distribution. The linear chain trick and a uctuation lemma are applied to obtain the global limiting behavior of the model. When each population can survive if it is cultured a...